Question

Find the sum of the multiples of 6 from 200 to 1100

Answer 1

❤❤Hey!!❤❤

First multiple after 200 = 204

Last multiple before 1100 = 1098

Here first term a = 204

Common Difference d = 6

Last term an = 1098

an = a + ( n - 1 )* d

=> 1098 = 204 + ( n - 1 ) * 6

=> 1098 = 204 + 6n - 6

=> 1098 = 198 + 6n

=> 1098 - 198 = 6n

=> 900 = 6n

=> 900 / 6 = n

=> n = 150

We know that the last sum of nth term is

Sn = n / 2 [ a + l ]

=> S150 = 150 / 2 [ 204 + 1098 ]

=> S150 = 75 × 1302


=> S150 = 97650.

Therefore, the sum of the multiples of 6 from 200 to 1100 is 97650.

Hope it helps!